Simplify the following expression: $p = \dfrac{-3n^2 - 6n + 9}{n + 3} $
Answer: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-3$ , so we can rewrite the expression: $ p =\dfrac{-3(n^2 + 2n - 3)}{n + 3} $ Then we factor the remaining polynomial: $n^2 + {2}n {-3} $ ${3} {-1} = {2}$ ${3} \times {-1} = {-3}$ $ (n + {3}) (n {-1}) $ This gives us a factored expression: $\dfrac{-3(n + {3}) (n {-1})}{n + 3}$ We can divide the numerator and denominator by $(n - 3)$ on condition that $n \neq -3$ Therefore $p = -3(n - 1); n \neq -3$